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PHYSICAL SCIENCES / BIOLOGICAL SCIENCES / PHYSICS / BIOPHYSICS
Internal strain regulates the nucleotide binding site of the kinesin leading head
Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0374
Contributed by José N. Onuchic, December 9, 2006 (received for review November 28, 2006)
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-based kinesin structure whose motor domains are bound on the tubulin binding sites. The equilibrium structures of kinesin on the microtubule show disordered and ordered neck-linker configurations for the L and trailing head, respectively. The comparison of the structures between the two heads shows that several native contacts present at the nucleotide binding site in the L are less intact than those in the binding site of the rear head. The network of native contacts obtained from this comparison provides the internal tension propagation pathway, which leads to the disruption of the nucleotide binding site in the L. Also, using an argument based on polymer theory, we estimate the internal tension built on the neck-linker to be f 
12–15 pN. Both of these conclusions support the experimental hypothesis.
cracking | internal strain-induced regulation | microtubule | processivity
One of the experimentally best studied molecular motors is the conventional kinesin (kinesin-1) (18, 19), a relatively small motor protein that transports cellular materials by walking in an unidirectional hand-over-hand manner along the microtubule (MT) filaments. Compared with other motor proteins involved in material transport, such as myosin and dynein, the conventional kinesin has a remarkable processivity and can travel 100 steps (8.2 nm) without being dissociated from the MT. The mechanochemical cycle conjectured from experiments suggests that there must be a dynamic coordination between the two motor domains to achieve such high processivity. The quest to identify the origin of this dynamic coordination has drawn extensive attention from the kinesin community. Since Hancock and Howard (20) first hypothesized that the "internal strain" was needed for processivity, the strain-dependent mechanochemistry became a popular subject in kinesin studies (21–23). With the aid of optical tweezers, Guydosh and Block (24) recently revisited this issue by monitoring the real-time kinesin dynamics in the presence of ATP and ADP·BeFx, a tight binding ATP analog (24). They discovered that, when ADP·BeFx was bound to the kinesin, the pause time of the step increased substantially and that the normal step was restored only after the obligatory backstep. This finding suggests that ADP·BeFx is released only when the head bound with ADP·BeFx becomes the leading head (L). Supported by this observation, they advocated a kinetic model in which the rearward strain via the neck-linker facilitates the release of the ligand from the L (24). Stated differently, the binding of the ligand to the L is inhibited because the rearward strain constitutes an unfavorable environment for the ATP binding sites of the L. In the present study, we focus on the elucidation of the structural origin of the coordinated motion in kinesin by adopting a simple computational strategy.
Better straightforward evidence of the regulation on the nucleotide binding site can be obtained when a structure in which both kinesin heads are simultaneously bound to the MT binding site is determined. Such a structure will allow us to identify the structural differences between the L and the trailing head (T). To date, this structure, however, has not yet been reported. The only available structures include an isolated kinesin-1 without the MT (6), an isolated single-headed kinesin-like (KIF1A) with various ligand states (7), and a single KIF1A bound to the tubulin-dimer binding site (25). Therefore, we used existing Protein Data Bank (PDB) structures and manually built a model system of the two-headed kinesin molecule with both heads bound to the tubulin binding sites (see Fig. 2). This model was used to generate an ensemble of structures via simulations. A direct comparison between the L and T equilibrium structures shows that the tension built on the neck-linker induces the disruption of the nucleotide binding site of the L, which directly supports inferences from experimental observations (23–24).
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(ii)]. Docking of the neck-linker to the neck-linker binding motif on the L (X in Fig. 1) propels the T (Y in Fig. 1) in the (+)-direction of MT, which leads to an 8 nm mechanical step [(ii) 
(ii')]. The interaction with the MT facilitates the dissociation of ADP from the catalytic core of L [(ii' (iii)]. ATP is hydrolyzed and produces ADP·Pi state for the T [(iii) (iv)]. When Pi is released and the T is unbound from the MT, the half-cycle is completed [(iv) (i)]. The mechanical step is achieved in a hand-over-hand fashion by alternating the binding of the two motor domains (X and Y in Fig. 1) to the MT (29, 30). High processivity of the kinesin requires this kinetic cycle to be stable (remain within the yellow box in Fig. 1). A premature binding of the ATP to the L in the state of (E:MT) should be prevented, i.e., the condition k
[ATP]/(k
+ k
) and k
[ATP]/(k
+ k
) 0 should be satisfied in Fig. 1 [see supporting information (SI) Text for the master equation describing the kinetic cycle]. ATP binding to the (iii) or (iv) states can destroy the mechanochemical cycle of the kinesin. The binding of ATP on the L should be suppressed before the 
-Pi is released from the T. Otherwise, both heads become ADP-bound states, which have a weak binding affinity to the MT and lead to dissociation from the MT. Because the kinesin has a high processivity compared with other molecular motors, effective communication is required between the two heads regarding the chemical state of each of the partner motor domains.
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9 and 10) and the neck-linker binding site on the motor domain (7). To this end, we manipulated the 3D structure of 3KIN around the neck-linker of the L and created a temporary structure whose two heads bind to the MT binding sites simultaneously. Both L and T have energetic biases toward the identical native fold, but the interactions with the tubulin binding sites adapt the dimeric kinesin structure into a different minimum structure, which is not known a priori. We performed simulations (see Methods) to relax this initial structure and to establish the thermal equilibrium ensemble of the kinesin molecule on MT (see Fig. 3A). Transient dimeric kinesin conformations corresponding to the steps (iii) and (iv) during the cycle (Fig. 1) allow us to investigate the structural deviation between L and T of the kinesin molecule. This simple computational exercise can confirm or dismiss the experimental conjecture regarding whether the mechanochemical strain significantly induces regulation on the nucleotide binding site and whether it occurs in the L.
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Global shape comparison.
There are in principle multiple ways to quantitatively compare the two motor domain structures. To assess the structural differences, the radius of gyration [R
= 1/2N2
i, j(
i – j)2] of the two motor domain structures from the equilibrium ensemble are computed (see Fig. 3B). Because the neck-linker and the neck-helix adopt different configurations relative to the motor domain in each monomer, we perform an Rg analysis for the motor domains only (residues 2–324). The Rg distributions show that the L is slightly bigger than the T both in the size {[
Rg
(L) – Rg(T)] 
0.4 Å} and in the dispersion [(
L – T) 0.05 Å]. Meanwhile, the Rg for the native state (3KIN) is R
= 19.4 Å. Clearly, the sizes of both of the heads in the thermal ensemble are expanded at T = 300 K as compared with the native structure. The size alone does not tell much about the difference between the structures.
The rmsd relative to the native structure and between the two motor domains (residues 2–324) computed over the equilibrium ensemble gives rmsd(T|native) = 2.0 Å, rmsd(L|native) = 9.4 Å, rmsd(T|L) = 9.6 Å, where rmsd(X|Y) is the rmsd between conformations X and Y. If the 6 helix is excluded from the rmsd calculation of motor domain (residues 2–315), then rmsd(T|native) 1.8 Å, rmsd(L|native) 3.8 Å, and rmsd(T|L) 3.9 Å. The rmsd analysis shows that the 6 helix significantly contributes more for the deviation of the L from its native state than does the T.
Additional detailed comparisons with respect to the native state can be made by using the structural overlap function of the i – j pair, 
ij, which is defined as ij = 
(Rij – R
) where (Rij – R) = 1 if |Rij – R| < rtol; otherwise (Rij – R) = 0. R is the distance of the i – j pair in native state, where rtol = 1 Å. By setting R values identical in both heads (i.e., both heads have the same native state), we compute the ij values for the T and the L, respectively. The relative difference of the ij value between T and L, Xij, is defined as
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which quantitatively measures the structural difference of the two heads. Based on the Xij value (Fig. 3C), the distances between the MT binding motif of the T (L11, L12, 4, and 5) and other secondary structure units (1, 0, 2, 1, 2, and 3) are 50% more native-like than in the L.
Conserved native contacts in T reveal the strain propagation pathway in L.
A direct measurement of similarity to the native structure is the fraction of native contacts preserved in the thermal ensemble (31). Because we assume that ATP affinity is optimized in the native state, we can readily assess the quality of the structure by using this measure. We quantify the nativeness of a pair by using qij(
) = 
(Rc – Rij)
ij, where ij = 1 if i, j residues are in contact at the native state (R < R
= 8 Å), and ij = 0 otherwise. qij() (with = T or L) is obtained by averaging over the thermal ensemble. When qij() is averaged over all of the native pairs, the average fraction of native contacts, Q, is calculated as Q() = 1/NQ
qij(), where NQ is the total number of native pairs. For the T and L conformations, Q(T) = 0.86 and Q(L) = 0.82, respectively. The relative difference of native contacts between the two kinesin heads at the pair level, Qij, is quantified similarly to Eq. 1 as
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In Fig. 4, Qij is color-coded based on its value. As expected from the equilibrium ensemble, conspicuous differences are found around the structural motifs having direct contacts with neck-linker, giving Qij 
0.5. Quantitative inspection of the other contacts is illustrated in the structure. We color the kinesin head structure based on the Qij value. The residue pairs are colored in magenta if 0.2 < Qij < 0.5 and red if Qij > 0.5, where the positive Qij signifies that the native contacts in T are more intact. The residue pairs are colored in light-blue if –0.5 < Qij < –0.2 and blue if Qij < –0.5. More intact contacts, when the T and the L are compared, are visualized by the yellow line in Fig. 5B. Our analysis not only shows that there is higher probability of the formation of native contacts present in the T in comparison to the L but also suggests how the tension is propagated toward the nucleotide binding site to disrupt the nativeness of the nucleotide binding pocket in the L. As expected, a dense network of intact contacts are found between the neck-linker (10) and the neck-linker binding motif (7). This network continues along the 6 helix, perturbing L2, 1, and 4, and finally reaches the nucleotide binding site (see SI Fig. 6 for the nomenclatures of the secondary structures). It is surprising that the disruptions of native contacts are found particularly in the nucleotide binding site, which is believed to be the trigger point for the allosteric transition. All of the important nucleotide binding motifs (P-loop, switch-1, switch-2, and N4) are recognized by our simulational analysis using a nonlinear Hamiltonian (see SI Figs. 7 and 8 and SI Text for the comparison with linear harmonic potential represented as a Gaussian network model).
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where lp is the persistence length of the polymer and L is the contour length. L 5.7 nm for the 15-aa neck-linker (residues 324–338) (= 15 x 0.38 nm), and in the equilibrium ensemble of structures, x 3.1 ± 0.8 nm. Assuming that lp 0.4–0.5 nm (33) for this segment, we estimate a tension f = 12–15 pN. By integrating Eq. 3 for 0–3.1 nm, the tensional energy stored in the neck-linker is obtained, which is 17 pN·nm 4 kBT. Approximately 20% of the ATP hydrolysis energy (25 kBT) is stored in the neck-linker and directly perturbs the nucleotide binding site of the L, whereas mechanical action to the T is dissipated through the dense network of contacts formed between the neck-linker (10) and the neck-linker binding site (7).
For a given extension x when the length of the neck-linker is varied by L, the variation in the length of the neck-linker can affect the effective tension as f(L + L) – f(L) –kBT/lp{1/[4(1 – x/L)2] x (2x/L)/(1 – x/L) + x/L}(L/L). For a given L/L, the resulting tension change may be significant depending on the value of the extension x. Experimentally, the kinesin dynamics has recently been studied by varying the linker length by introducing a spacer composed of amino acids (34). Because L = 0.38 nm for the insertion of a single amino acid, the lengthening of the linker leads to a reduction of the tension by f –2 pN. In light of the force values controlling the kinesin dynamics in laser optical tweezers experiments, which are 0–7 pN and because 7 pN is the stall force, a value of f –2 pN can be significant. According to the experimental analysis performed by Hackney et al. (34), the processivity is reduced by 2-fold when a single amino acid is inserted or deleted, and 6 or 12 additional amino acids resulted in a 3- to 4-fold reduction in the kinetic processivity.
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(iii) in Fig. 1. The latter point is consistent with the experimental observation of Uemura and Ishiwata (21) of a 7-fold increase of the ADP dissociation constant from the monomeric kinesin head in the presence of rearward loading (21). It is noteworthy that global measures characterizing two-head domains do not distinguish the qualitative differences between the two heads. Major changes in the strained region, such as to the kinesin neck-linker, may be associated to minor global differences in the motor domain. Exactly how these minor global differences that are localized in a small volume are amplified in the process of allosteric transition is another key issue in understanding molecular motors.
Internal tension regulates the interaction between the kinesin and the nucleotide. Conversely, the interaction between kinesin, nucleotide, and MT also switches the internal tension on and off. For conventional kinesin, mechanical and chemical mechanism are closely correlated, producing a remarkable processivity of kinesin movement on the MT.
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–5, and results from the self-organized polymer potential are in SI Fig. 9. This suggests that the results are robust as long as the information of native topology with a nonlinear form of energy potential is used as an input.
Energy Function–SB Potential.
Using the structure in Fig. 2C as a starting structure, we simulated and sampled an ensemble of two-headed kinesin configurations on the MT. We performed Langevin simulations of the SB model (40), whose equation of the motion of each interaction center is integrated by a Verlet algorithm. The energy potential is given as
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where the energy Hamiltonian is divided into intramolecular interactions for the kinesin molecule and intermolecular interactions at the kinesin–MT interface. The superscripts K and tub denote the kinesin and the kinesin–tubulin interaction, respectively. Because our focus is on the kinesin dynamics, we fixed the coordinates of the MT in space. Because the length scale of the kinesin geometry is small (<10 nm) compared with that of MT (diameter, 24 nm; persistence length, 1 mm), the explicit computation of the dynamics of the entire MT structure, in which the 13 protofilaments constitute the cylindrical geometry, should not qualitatively change our conclusions. The first and the second term define the backbone interactions. The bond distance ri,i+1 between the neighboring residues i and i + 1 are harmonically constrained with respect to the bond distance in native state r
with a strength Kr = 20 kcal/(mol·Å2). In the second term, the angle 
is formed between residues i, i + 1, and i + 2, with K = 20 kcal/(mol·rad2). 
is the angle of the native state. The third term is the dihedral angle potential with K
= 1.0 kcal/mol and K
= 0.5 kcal/mol that describes the ease of rotation around the angle formed between successive residues from i to i + 3 to along the backbone. The Lennard–Jones potential is used to account for the interactions that stabilize the native topology. A native contact is defined from the pair of interaction centers whose distance is R
8 Å in native state for |i – j| > 2. If i and j residues are in contact in the native state, ij = 1; otherwise ij = 0. Aided by ij we assign stabilizing potential for native pairs and repulsive potential for nonnative pairs. We assign 
h = 1.8 kcal/mol for the intraneck and interneck helix (residue > 338) interactions to secure the coiled-coil association between the neck-helices. For other kinesin residue–residue interactions, we set h = l = 1.0 kcal/mol regardless of the sequence identity. The parameters determining the native topology , 
, r, and ij are determined from the crystal structure of human kinesin (PDB ID 3KIN) and incorporated to the T kinesin and the coiled-coil whose structure is shown in Fig. 2C. To constitute an identical fold condition, we transferred topological information in T to the L by substituting , , r, and ij from T to L; i.e., (L) = (T), (L) = (T), r(L) = r(T), and ij(L) = ij(T) for all i and j. The kinesin–tubulin interaction parameters (h, l, r
, and ik) are similarly defined as kinesin intramolecular interaction parameters except for the slightly larger native contact distance (R
= 10 Å). The parameters r and 
* defining the interface topology between the T kinesin and the tubulin also are transferred to the interface topology between the L and the next tubulin binding site.
Simulations.
The initial structure, whose two heads are constrained to be oriented on the tubulin binding sites, is relaxed under the SB or self-organized polymer Hamiltonian, and subsequently the equilibrium ensemble of the structures is collected from the low-friction Langevin dynamics simulations at T = 300 K. The position of the interaction center is integrated by using
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where 
is friction coefficient,–
H/r
is the conformation force, and 
is the random force satisfying (t)·(t') = (6kBT/h)(t – t') where the integration time (h) is discretized. In low-friction Langevin dynamics, natural time is given by 
L = (ma2/h)1/2. We chose = 0.05
and h = 0.0025L. Low friction is deliberately chosen for the purpose of effectively sampling the conformational space (43). Under such conditions, the resulting dynamics as a function of time step should not be taken parallel to the real-time dynamics. To produce an overdamped dynamics, it is essential to integrate the motion by neglecting the inertial term as well as choosing a high-friction coefficient that amounts to the water viscosity (1cP).
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Abbreviations: L, leading head; MT, microtubule; T, trailing head; SB, structure-based.
To whom correspondence should be addressed at: Center for Theoretical Biological Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0374. E-mail: jonuchic{at}ucsd.edu
Author contributions: C.H. and J.N.O. designed research; C.H. performed research; C.H. and J.N.O. analyzed data; and C.H. and J.N.O. wrote the paper.
The authors declare no conflict of interest.
This article contains supporting information online at www.pnas.org/cgi/content/full/0610939104/DC1.
© 2007 by The National Academy of Sciences of the USA
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